In the GatePass Demo version, you can go directly to the next stage from the door in the stage.
A real-life player pointed out to me that I should be able to go to the next stage as soon as I clear a stage, so I changed the setting to try it out.
I made the change only for the trial version, but it seems to be going smoother than I expected. If it looks OK, I'll try changing the door position in the regular Steam version as well.
Only the Windows version is being updated; the Mac version will be updated at a later date.